Statistics and Probability Concepts
 Elementary School The student produces evidence that demonstrates understanding of statistics and probability concepts in the following areas; that is, the student: a Collects and organizes data to answer a question or test a hypothesis by comparing sets of data. b Displays data in line plots, graphs, tables, and charts. c Makes statements and draws simple conclusions based on data; that is: • reads data in line plots, graphs, tables, and charts; • compares data in order to make true statements, e.g., “seven plants grew at least 5 cm”; • identifies and uses the mode necessary for making true statements, e.g., “more people chose red”; • makes true statements based on a simple concept of average (median and mean), for a small sample size and where the situation is made evident with concrete materials or clear representations; • interprets data to determine the reasonableness of statements about the data, e.g., “twice as often,” “three times faster”; • uses data, including statements about the data, to make a simple concluding statement about a situation, e.g., “This kind of plant grows better near sunlight because the seven plants that were near the window grew at least 5 cm.” d Gathers data about an entire group or by sampling group members to understand the concept of sample, i.e., that a large sample leads to more reliable information, e.g., when flipping coins. e Predicts results, analyzes data, and finds out why some results are more likely, less likely, or equally likely. e Finds all possible combinations and arrangements within certain constraints involving a limited number of variables.

 Middle School The student produces evidence that demonstrates understanding of statistics and probability concepts; that is, the student: a Collects data, organizes data, and displays data with tables, charts, and graphs that are appropriate, i.e., consistent with the nature of the data. b Analyzes data with respect to characteristics of frequency and distribution, including mode and range. c Analyzes appropriately central tendencies of data by considering mean and median. d Makes conclusions and recommendations based on data analysis. e Critiques the conclusions and recommendations of others’ statistics. f Considers the effects of missing or incorrect information. g Formulates hypotheses to answer a question and uses data to test hypotheses. h Represents and determines probability as a fraction of a set of equally likely outcomes; recognizes equally likely outcomes, and constructs sample spaces (including those described by numerical combinations and permutations). i Makes predictions based on experimental or theoretical probabilities. j Predicts the result of a series of trials once the probability for one trial is known.

 High School The student demonstrates understanding of statistics and probability concepts; that is, the student: a Organizes, analyzes, and displays single-variable data, choosing appropriate frequency distributions, circle graphs, line plots, histograms, and summary statistics. b Organizes, analyzes, and displays two-variable data using scatter plots, estimated regression lines, and computer generated regression lines and correlation coefficients. c Uses sampling techniques to draw inferences about large populations. d Understands that making an inference about a population from a sample always involves uncertainty and that the role of statistics is to estimate the size of that uncertainty. e Formulates hypotheses to answer a question and uses data to test hypotheses. f Interprets representations of data, compares distributions of data, and critiques conclusions and the use of statistics, both in school materials and in public documents. g Explores questions of experimental design, use of control groups, and reliability. h Creates and uses models of probabilistic situations and understands the role of assumptions in this process. i Uses concepts such as equally likely, sample space, outcome, and event in analyzing situations involving chance. j Constructs appropriate sample spaces, and applies the addition and multiplication principles for probabilities. k Uses the concept of a probability distribution to discuss whether an event is rare or reasonably likely. l Chooses an appropriate probability model and uses it to arrive at a theoretical probability for a chance event. m Uses relative frequencies based on empirical data to arrive at an experimental probability for a chance event. n Designs simulations including Monte Carlo simulations to estimate probabilities. o Works with the normal distribution in some of its basic applications.